Working at the same rate, 6 men can do 3/5 of a job...

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Poisson: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Sat Aug 11, 2012 1:31 am

by Poisson » Wed Dec 28, 2016 8:31 am

Working at the same rate, 6 men can do 3/5 of a job in 20 minutes. At this rate, how many minutes would it take one man to do 1/4 of the job?

A. 30 minutes
B. 40 minutes
C. 50 minutes
D. 60 minutes
E. 70 minutes

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Source: Beat The GMAT — Problem Solving | Wed Dec 28, 2016 8:31 am

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by Brent@GMATPrepNow » Wed Dec 28, 2016 8:41 am

Poisson wrote:Working at the same rate, 6 men can do 3/5 of a job in 20 minutes. At this rate, how many minutes would it take one man to do 1/4 of the job?

A. 30 minutes
B. 40 minutes
C. 50 minutes
D. 60 minutes
E. 70 minutes

6 men can do 3/5 of a job in 20 minutes
So, 1 MAN can do 3/30 of a job in 20 minutes [divided 6 men by 6, and divided 3/5 by 6]
In other words, 1 MAN can do 1/10 of a job in 20 minutes

This means that, 1 MAN can do 2/10 of a job in 40 minutes
And 1 MAN can do 3/10 of a job in 60 minutes

Since 1/4 lies BETWEEN 2/20 and 3/10, we can conclude that it takes more than 40 minutes and less then 60 minutes to complete 1/4 of the job.

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Dec 28, 2016 10:00 am

Poisson wrote:Working at the same rate, 6 men can do 3/5 of a job in 20 minutes. At this rate, how many minutes would it take one man to do 1/4 of the job?

A. 30 minutes
B. 40 minutes
C. 50 minutes
D. 60 minutes
E. 70 minutes

We can use the following formula:

(number of workers)(number of minutes)/output = (number of workers)(number of minutes)/output

Let the job = the product of the two denominators = 5*4 = 20 units.

To produce 3/5 of the 20 units -- in other words, 12 units -- 6 men take 20 minutes.
We want to determine how many minutes are required for 1 worker to produce 1/4 of the 20 units -- in other words, 5 units.
Plugging these values into the formula above, we get:

(6*20)/12 = (1*x)/5

Solving the resulting equation, we get:
x = 50.

The correct answer is C.

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by [email protected] » Wed Dec 28, 2016 5:55 pm

Hi Poisson,

In these types of questions, it often helps to simplify the given information one 'step' at a time.

Here, we're told that 6 men can do 3/5 of a job in 20 minutes. We rewrite the fraction as 6/10...

6 men do 6/10 of a job in 20 minutes. It's important to note that each man works for 20 minutes, so the work that is done in those 20 minutes is divided by the 6 men...

1 man does 1/10 of a job in 20 minutes

Now we can 'work up' to the full job...

1 man does 1/1 of a job in 20(10) = 200 minutes.

The questions asks how long it would take one man to do 1/4 of the job. Since the full job would take 1 man 200 minutes, 1/4 of the job would take (1/4)(200) = 50 minutes.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Mon Jan 02, 2017 12:27 pm

Poisson wrote:Working at the same rate, 6 men can do 3/5 of a job in 20 minutes. At this rate, how many minutes would it take one man to do 1/4 of the job?

A. 30 minutes
B. 40 minutes
C. 50 minutes
D. 60 minutes
E. 70 minutes

A little old-fashioned algebra and our trusty formula R*T = W will do.

The rate for one man: r; The rate for 6 men: 6r
Time: 20 minutes or 1/3 of an hour
Work: 3/5 of a job
6r * (1/3) = 3/5; r = 3/10

We know r = 3/10
We want 't,' when w = 1/4
(3/10) * t = 1/4; t = 10/12 = 5/6; 5/6 of an hour = 50 minutes. Answer is C

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Wed Jan 04, 2017 7:22 am

Poisson wrote:Working at the same rate, 6 men can do 3/5 of a job in 20 minutes. At this rate, how many minutes would it take one man to do 1/4 of the job?

A. 30 minutes
B. 40 minutes
C. 50 minutes
D. 60 minutes
E. 70 minutes

We are given that 6 men can do 3/5 of a job in 20 minutes. Since rate = work/time, the rate of the 6 men is:

(3/5)/20 = (3/5) x (1/20) = 3/100

We need to determine the number of minutes for 1 man to complete 1/4 of the job.

Since the rate of 6 men is 3/100, we divide that rate to get the rate for 1 man:

(3/100)/6 = (3/100) x (1/6) = 1/200

Finally, we can determine how long it would take 1 man to complete 1/4 of the job.

time = work/rate

time = (1/4)/(1/200) = (1/4) x (200/1) = 50 minutes

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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Yemunn Soe: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon May 01, 2017 10:33 pm

by Yemunn Soe » Mon May 08, 2017 5:21 pm

Working @ same rate,

Together they will take 3/5(60%) of the work to be done in 20) minutes.

Each man will take 3/5(60%) of the work to be done in 120(6x20) minutes.

(Same work load/done but it will take more time for each)

Together 60% in 20 min
Together 6% in 2 min
Together 3% in 1 min
Together 1% in ...
Together (1/4) or 25% in 25 min

Each 60% in 120(6x20) min
Each 6% in 12 min
Each 3% in 6 min
Each 1% in 2 min
Each 25% in 50 min

The concept is get 1% of together work done and than each man work done.

The correct answer is 50 minutes

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